Characterization of dielectric function for metallic thin films based on ellipsometric parameters and reflectivity

A synergic analysis method based on ellipsometric parameters and reflectivity is proposed to simultaneously determine the thickness and the thickness-dependent dielectric functions of metallic thin films on the opaque substrate. Both the ellipsometric parameters and reflectivity are measured by one spectroscopic ellipsometer. The proposed method consists of a point-by-point synergic regression analysis on the ellipsometric parameters and the reflectivity as well as an oscillator-parametrization regression analysis on the ellipsometric parameters. The oscillator-parametrization model is composed of the Drude oscillator, two TaucLorentz oscillators and a Lorentz oscillator, which describe the intraband, the interband and the plasmon contributions to the dielectric functions, respectively. Practical measurement experiments on a series of Cu thin films deposited on Si substrates have been carried out for demonstration, in which a broad spectral range of 0.73-4.96 eV has been covered. The relative deviations between the thicknesses reported by our method and reported by Atomic Force Microscopy and Transmission Electron Microscopy are less than 3.5%, which verifies the validity and the accuracy of the proposed method. Meanwhile, the results of oscillator-parametrization regression analysis indicate that both the real part epsilon(1) and the imaginary part epsilon(2) of the dielectric functions decrease with the increasing Cu film thickness in the range of 6.8-12.9 nm. Besides, the fitting results also exhibits that both the plasma energy and the Drude relaxation time increase monotonically with the thickness increasing, in which the increasing of Drude relaxation time can be attributed to the increasing of surface scattering time.